Advanced Calculus : An Introduction to Classical Analysis

Louis Brand

ISBN 10: 0486445488 / ISBN 13: 9780486445489

Editore: Dover Publications Jan 2006, 2006

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Neuware - A course in analysis dealing essentially with functions of a real variable, this text for upper-level undergraduate students introduces the basic concepts in their simplest setting and proceeds with numerous examples, theorems stated in a practical manner, and coherently expressed proofs. 1955 edition.

Codice articolo 9780486445489

Dati bibliografici

• Titolo: Advanced Calculus : An Introduction to Classical Analysis
• Editore: Dover Publications Jan 2006
• Data di pubblicazione: 2006
• Lingua: Inglese
• ISBN 10: 0486445488
• ISBN 13: 9780486445489
• Rilegatura: Taschenbuch
• Condizione: Neu

Descrizione articolo

Riassunto

A course in analysis that focuses on the functions of a real variable, this text is geared toward upper-level undergraduate students. It introduces the basic concepts in their simplest setting and illustrates its teachings with numerous examples, practical theorems, and coherent proofs.
Starting with the structure of the system of real and complex numbers, the text deals at length with the convergence of sequences and series and explores the functions of a real variable and of several variables. Subsequent chapters offer a brief and self-contained introduction to vectors that covers important aspects, including gradients, divergence, and rotation. An entire chapter is devoted to the reversal of order in limiting processes, and the treatment concludes with an examination of Fourier series.

Contenuti

1. The Number System 2. Sequences and Series 3. Functions of a Real Variable 4. Functions of Several Variables 5. Vectors 6. The Definite Integral 7. Improper Integrals 8. Line Integrals 9. Multiple Integrals 10. Uniform Convergence 11. Functions of a Complex Variable 12. Fourier Series Appendixes Comprehensive Test Answers to Problems Index